Inkscape on Windows 7 fails to start

Many people have reported similar issues, in most cases it would appear to be a conflict with another piece of software.

This means you'll have to think what you installed around the same time.

It appears others have had issues (and had to uninstall)

Adobe Dreamweaver
Scribus
Ghostscript
(this list is not complete)

For some people the fix was Windows Updates, others was a different build (download the latest version), for some a reinstall (although that doesn't work for you) and for some, it's just started to work again with no way to diagnose cause or resolution!

One person found a fix (which helped many others), they wrote

Then I replaced liblcms-1.dll with the one found at http://cue.yellowmagic.info/softwares/separate-plus/index.html and it now works. I noticed when I attached the MS debugger that there was a little warning that it did not load this dll at the default location, so some other install/security fix may have changed this and indirectly caused the problem.

Source